Wave propagation in laminated structure through wave finite element method

Abstract

In this paper, the wave finite element(WFE) method is briefly presented and applied in order to extract the dispersion curves. The formulation of the laminated structure is detailed through the Timoshenko theory. The finite element technique is used to model the laminated beam and extract the mass and stiffness matrices for the bending vibration. The bending vibration of the laminated beam is simulated and discussed. The travelling and evanescent modes are illustrated to characterize the flexural wave propagation in laminated structure. The resolution of the equilibrium equation leads to the extraction of the analytical wave number as a function of the frequency in order to validate the dispersion curves simulated through the WFE method. The question of the influence of the layers thickness on the wave propagation is detailed. An uncertainty is introduced in the thickness as a Gaussian variable and the mean and the standard deviation of the dispersion curves are extracted through the Monte Carlo simulation. Among the contributions of this article, the laminated structures are modeled through the Abaqus software and the mass and stiffness matrices are extracted for the multimodal propagation. The multimodal wave number is presented and discussed for the travelling and evanescent modes.